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<p>To understand vector fields, it is best to look at the equation of motion:</p>

<p><font size="5">dz</font><font size="5">/dt = F(z)</font></p>

<p>If we integrate for a time t=0, we just obtain the identity map! In FPP, if 
we declared a quantity Id as a DAMAP, we can make it into the identity either 
with </p>
<dl>
  <dd><font face="Courier">Id=1 </font></dd>
</dl>

<p>or manually with the loop</p>
<dl>
  <dd>

<p align="left"><font face="Courier">do i=1,c_%nd2</font></p>
  </dd>
  <dd>

<p align="left"><font face="Courier">Id%v(i)=1.d0.mono.i</font></p>
  </dd>
  <dd>

<p align="left"><font face="Courier">enddo</font></p>
  </dd>
</dl>

<p>Now, the solution for a time t<font face="Times New Roman">&#8800;0, can be 
obtained from F as follows:</font></p>
<dl>
  <dd><span lang="EN-US" style="font-size: 10.5pt; font-family: Century">
  <!--[if gte mso 9]><xml>
 <o:OLEObject Type="Embed" ProgID="Equation" ShapeID="_x0000_i1025" DrawAspect="Content" ObjectID="_1161775000">
 </o:OLEObject>
</xml><img border="0" src="big_ta1.gif" width="265" height="52"><![endif]--></span></dd>
</dl>

<p>This is at the core of some Taylor series code such as the code
<a href="http://bt.pa.msu.edu/index_files/cosy.htm" style="font-weight: 700">
COSY</a> of Berz and collaborators.</p>
<p>A simple FODO cell of ideal quadrupoles is produced in the following FPP 
example. </p>
<p>&nbsp;</p>
<p align="center">
<a style="text-decoration: none" href="../simple_programs/z_vecfields_fodo.f90">
<b><font color="#FF0000" size="5">Click here for example</font></b></a></p>
<p>&nbsp;</p>
<p>&nbsp;</p>
<p align="center">&nbsp;</p>

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